Quadratic Equations Set – 7

1. I. 3x2 – 17x + 10 = 0
II. 3y2 + 4y – 4 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option C
Solution: 

3x2 – 17x + 10 = 0
3x2 – 15x – 2x + 10 = 0
Gives x = 2/3, 5
3y2 + 4y – 4 = 0
3y2 + 6y – 2y – 4 = 0
Gives y = -2, 2/3
Put all values on number line and analyze the relationship
-2…. 2/3…… 5

 

2. I. 3x2 – 14x + 8 = 0
II. 3y2 – 20y + 12 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

3x2 – 14x +8 = 0
3x2 – 12x – 2x + 8 = 0
Gives x = 2/3, 4
3y2 – 20y + 12 = 0
3y2 – 18y – 2y + 12 = 0
Gives y = 6, 2/3
Put all values on number line and analyze the relationship
2/3….. 4….. 6

 

3. I. 3x2 – 19x + 28 = 0
II. 4y2 – 5y – 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

4x2 – 19x + 28 = 0
4x2 – 12x – 7x + 28 = 0
Gives x = 7/3, 4
4y2 – 5y – 6 = 0
4y2 – 8y + 3y – 6 = 0
Gives y = -3/4, 2
Put all values on number line and analyze the relationship
-3/4…… 2…… 7/3…. 4

 

4. I. 6x2 + 23x + 21 = 0
II. 3y2 – 14y – 5 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option B
Solution: 

6x2 + 23x + 21 = 0
6x2 + 9x + 14x + 21 = 0
Gives x = -7/3, -3/2
3y2 – 14y – 5 = 0
3y2 – 15y + y – 5 = 0
Gives y = -1/3, 5
Put all values on number line and analyze the relationship
-7/3…… -3/2….. -1/3…… 5

 

5. I. 2x2 – 7x + 3 = 0
II. 2y2 + 11y + 12 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

2x2 – 7x + 3 = 0
2x2 – 6x – x + 3 = 0
Gives x = 3, 1/2
2y2 + 11y + 12 = 0
2y2 + 8y + 3y + 12 = 0
Gives y = -3/2, -4
Put all values on number line and analyze the relationship
-4……. -3/2…… 1/2….. 3

 

6. I. 3x2 + 22x + 35 = 0
II. 6y2 + 11y – 7 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

3x2 + 22x + 35 = 0
3x2 + 15x + 7x + 35 = 0
Gives x = -5, -7/3
6y2 + 11y – 7 = 0
6y2 – 3y + 14y – 7 = 0
Gives y = 1/2, -7/3
Put all values on number line and analyze the relationship
-5….. -7/3….. 1/2

 

7. I. 2x2 – 3x – 9 = 0
II. 3y2 + 11y + 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

2x2 – 3x – 9 = 0
2x2 – 6x + 3x – 9 = 0
Gives x = -3/2, 3
3y2 + 11y + 6 = 0
3y2 + 9y + 2y + 6 = 0
Gives y = -3, -2/3
Put all values on number line and analyze the relationship
-3….. -3/2….. -2/3…. 3

 

8. I. x2 + 14x + 45 = 0
II. 3y2 – y – 10 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option B
Solution: 

x2 + 14x + 45 = 0
x2 + 9x + 5x + 45 = 0
Gives x = -9, -5
3y2 – y – 10 = 0
3y2 – 6y + 5y – 10 = 0
Gives y = -5/3, 2
Put all values on number line and analyze the relationship
-9…….. -5….. -5/3……. 2

 

9. I. 4x2 + 17x + 15 = 0
II. 4y2 – 3y – 10 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

4x2 + 17x + 15 = 0
4x2 + 12x + 5x + 15 = 0
Gives x = -3, -5/4
4y2 – 3y – 10 = 0
4y2 – 8y + 5y – 10 = 0
Gives y = -5/4, 2
Put all values on number line and analyze the relationship
-3…… -5/4…… 2

 

10. I. 2x2 – 17x + 36 = 0
II. 3y2 – 14y + 8 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option C
Solution: 

2x2 – 17x + 36 = 0
2x2 – 8x – 9x + 36 = 0
Gives x = 4, 9/2
3y2 – 14y + 8 = 0
3y2 – 12y + 2y + 8 = 0
Gives y = 2/3, 4
Put all values on number line and analyze the relationship
2/3…… 4…… 9/2

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